摘要：30．已知:如图14.抛物线与轴交于点.点.与直线相交于点.点.直线与轴交于点． (1)写出直线的解析式． (2)求的面积． (3)若点在线段上以每秒1个单位长度的速度从向运动(不与重合).同时.点在射线上以每秒2个单位长度的速度从向运动．设运动时间为秒.请写出的面积与的函数关系式.并求出点运动多少时间时.的面积最大.最大面积是多少? 解:(1)在中.令 . .··············································· 1分 又点在上 的解析式为·············································································· 2分 (2)由.得 ···················································· 4分 . .······························································································· 5分 ························································································· 6分 (3)过点作于点 ······························································································· 7分 ·········································································································· 8分 由直线可得: 在中...则 .······················································································· 9分 ···················································································· 10分 ····························································································· 11分 此抛物线开口向下.当时. 当点运动2秒时.的面积达到最大.最大为．···························· 12分

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